The article “Probabilistic risk Assessment of infrastructure networks Subjected to hurricanes” (12th International Conference on Applications of Statistics and Probability in Civil Engineering, 2015) suggests a uniform distribution as a model for the actual landfall position of the eye of a hurricane. Consider the random variable x = distance of actual landfall from predicted landfall. Suppose that a uniform distribution on the interval that ranges from 0 km to 400 km is a reasonable model for x. a. Draw the density curve for x. b. What is the height of the density curve? c. What is the probability that x is at most 100? d. What is the probability that x is between 200 and 300? Between 50 and 150? Why are these two probabilities equal?
> For each of the following choices, explain which one would result in a wider large-sample confidence interval for p: a. 90% confidence level or 95% confidence level b. n = 100 or n = 400
> Suppose that a city planning commission wants to know the proportion of city residents who support installing streetlights in the downtown area. Two different people independently selected random samples of city residents and used their sample data to co
> An article in the Chicago Tribune (August 29, 1999) reported that in a poll of residents of the Chicago suburbs, 43% felt that their financial situation had improved during the past year. The following statement is from the article: “The findings of this
> Business Insider reported that a study commissioned by eBay Motors found that nearly 40% of millennials who drive a car that is more than 5 years old have named their cars (“Millennials Have an Odd Habit When It Comes to Their Cars,” April 14, 2016). a.
> The USA Snapshot titled “Have a Nice Trip” (USA TODAY, November 17, 2015) summarized data from a survey of 1000 U.S. adults who had traveled by air at least once in the previous year. The Snapshot includes the following statement: “38% admit to yelling a
> The article “Most Americans Don’t Understand the Cloud, But They Should” (foxbusiness.com, October 17, 2016, retrieved November 12, 2016) reported that in a sample of 1000 people, 22% said they have pretended to know what the cloud is or how it works. As
> USA TODAY reported that the proportion of Americans who prefer cheese on their burgers is 0.84 (USA TODAY, September 7, 2016). This estimate was based on a survey of a representative sample of 1000 adult Americans. Calculate and interpret a margin of err
> Suppose that 935 smokers each received a nicotine patch, which delivers nicotine to the bloodstream at a much slower rate than cigarettes do. Dosage was decreased to 0 over a 12-week period. Of these 935 people, 245 were still not smoking 6 months after
> The USA Snapshot titled “Big Bang Theory” (USA TODAY, October 14, 2016) summarized data from a sample of 1003 American parents of children age 6 to 11 years. It reported that 53% of these parents view science-oriented TV shows as a good way to expose the
> The use of the formula for margin of error requires a large sample. For each of the following combinations of n and pˆ, indicate whether the sample size is large enough for use of this formula to be appropriate. a. n = 100 and pˆ = 0.70 b. n = 40 and
> The report “Parents, Teens and Digital Monitoring” (Pew Research Center, January 7, 2016, www.pewinternet .org/2016/01/07/parents-teens-and-digital-monitoring, retrieved May 5, 2017) reported that 61% of parents of teens aged 13 to 17 said that they had
> Consider taking a random sample from a population with p 5 0.70. a. What is the standard error of p ˆ for random samples of size 100? b. Would the standard error of pˆ be smaller for samples of size 100 or samples of size 400? c. Does decreasing the s
> A car manufacturer is interested in learning about the proportion of people purchasing one of its cars who plan to purchase another car of this brand in the future. A random sample of 400 of these people included 267 who said they would purchase this bra
> The report “The 2016 Consumer Financial Literacy Survey” (The National Foundation for Credit Counseling, www .nfcc.org, retrieved October 28, 2016) summarized data from a representative sample of 1668 adult Americans. When asked if they typically carry c
> The paper “Sleeping with Technology: Cognitive, Affective and Technology Usage Predictors of Sleep Problems Among College Students” (Sleep Health [2016]: 49–56) summarized data from a survey of a sample of college students. Of the 734 students surveyed,
> The use of the formula for margin of error requires a large sample. For each of the following combinations of n and pˆ, indicate whether the sample size is large enough for use of this formula to be appropriate. a. n = 50 and p ˆ = 0.30 b. n = 50 and p
> The report “2007 Electronic Monitoring & Surveillance Survey” (American Management Association) summarized a survey of 304 U.S. businesses. The report stated that 91 of the 304 businesses had fired workers for misuse of the Internet. Assume that this sam
> Consider taking a random sample from a population with p = 0.40. a. What is the standard error of pˆ for random samples of size 100? b. Would the standard error of pˆ be greater for samples of size 100 or samples of size 200? c. If the sample size wer
> A large online retailer is interested in learning about the proportion of customers making a purchase during a particular month who were satisfied with the online ordering process. A random sample of 600 of these customers included 492 who indicated they
> A researcher wants to estimate the proportion of property owners who would pay their property taxes one month early if given a $50 reduction in their tax bill. Would the standard error of the sample proportion pˆ be larger if the actual population propor
> A researcher wants to estimate the proportion of city residents who favor spending city funds to promote tourism. Would the standard error of the sample proportion pˆ be smaller for random samples of size n = 100 or random samples of size n = 200?
> A random sample will be selected from the population of all students enrolled at a large college. The sample proportion pˆ will be used to estimate p, the proportion of all students who use public transportation to travel to campus. For which of the foll
> If two statistics are available for estimating a population characteristic, under what circumstances might you choose a biased statistic over an unbiased statistic?
> A random sample will be selected from the population of all adult residents of a particular city. The sample proportion pˆ will be used to estimate p, the proportion of all adult residents who do not own a car. For which of the following situations will
> Use the formula for the standard error of pˆ to explain why increasing the sample size decreases the standard error.
> A researcher wants to estimate the proportion of students enrolled at a university who are registered to vote. Would the standard error of the sample proportion pˆ be larger if the actual population proportion was p = 0.4 or p = 0.8?
> Three different statistics are being considered for estimating a population characteristic. The sampling distributions of the three statistics are shown in the following illustration: Which statistic would you recommend? Explain your choice. Statist
> Three different statistics are being considered for estimating a population characteristic. The sampling distributions of the three statistics are shown in the following illustration: Which of these statistics are unbiased estimators of the population c
> For estimating a population characteristic, why is an unbiased statistic generally preferred over a biased statistic? Does unbiasedness alone guarantee that the estimate will be close to the actual value of the population characteristic? Explain.
> A random sample will be selected from the population of all adult residents of a particular city. The sample proportion pˆ will be used to estimate p, the proportion of all adult residents who are employed full time. For which of the following situations
> Use the formula for the standard error of pˆ to explain why a. the standard error is greater when the value of the population proportion p is near 0.5 than when it is near 1. b. the standard error of pˆ is the same when the value of the population prop
> A researcher wants to estimate the proportion of students enrolled at a university who eat fast food more than three times in a typical week. Would the standard error of the sample proportion pˆ be smaller for random samples of size n = 50 or random samp
> Three different statistics are being considered for estimating a population characteristic. The sampling distributions of the three statistics are shown in the following illustration: Which statistic would you recommend? Explain your choice. Statist
> Three different statistics are being considered for estimating a population characteristic. The sampling distributions of the three statistics are shown in the following illustration: Which of these statistics are unbiased estimators of the population ch
> For estimating a population characteristic, why is an unbiased statistic with a small standard error preferred over an unbiased statistic with a larger standard error?
> Determine the following standard normal (z) curve areas: a. The area under the z curve to the left of 1.75 b. The area under the z curve to the left of -0.68 c. The area under the z curve to the right of 1.20 d. The area under the z curve to the righ
> A business has six customer service telephone lines. Consider the random variable x 5 number of lines in use at a randomly selected time. Suppose that the probability distribution of x is as follows: a. Calculate the mean value and standard deviation of
> A company makes hardwood flooring, which it sells in boxes that will cover 500 square feet of floor. Let x = the number of boxes ordered by a randomly chosen customer. Suppose the probability distribution of x is as follows: a. Calculate and interpret th
> The probability distribution of x, the number of tires needing replacement on a randomly selected automobile checked at a certain inspection station, is given in the following table: The mean value of x is ux = 1.2. Calculate the values of σx
> A grocery store has an express line for customers purchasing at most five items. Consider the random variable x = the number of items purchased by a randomly selected customer using this line. Make two tables that represent two different possible probabi
> Suppose that for a given computer salesperson, the probability distribution of x 5 the number of systems sold in 1 week is given by the following table: a. Find the mean value of x (the mean number of systems sold). b. Find the variance and standard de
> A local television station sells 15-second, 30-s econd, and 60-second advertising spots. Consider the random variable x = length of a randomly selected commercial appearing on this station, and suppose that the probability distribution of x is given by t
> A grocery store has an express line for customers purchasing at most five items. Consider the random variable x = the number of items purchased by a randomly selected customer using this line. Make two tables that represent two different possible probabi
> An appliance dealer sells three different models of freezers having 13.5, 15.9, and 19.1 cubic feet of storage space. Consider the random variable x = the amount of storage space purchased by the next customer to buy a freezer. Suppose that x has the fol
> Consider the random variable y = the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose the probability distribution of y is as follows: a. Calculate and interpret my. (Hint: See Example 6.13.) b. In the long run, for what
> Refer to the probability distribution given in the previous exercise. Put the following probabilities in order, from smallest to largest: P(2 < x < 3) P(2 ≤ x ≤ 3) P(x < 2) P(x > 7) Explain your reasoning.
> A particular professor never dismisses class early. Let x denote the amount of additional time (in minutes) that elapses before the professor dismisses class. Suppose that x has a uniform distribution on the interval from 0 to 10 minutes. The density cur
> Refer to the probabilities given in Parts (a)–(d) of the previous exercise. Which of these probabilities is smallest? Which is largest? Data from exercise 6.28: The continuous random variable x has the probability distribution shown he
> The continuous random variable x has the probability distribution shown here: Shade the area under the curve corresponding to each of the following probabilities. (Draw a new curve for each part.) a. P(x b. P(x > 3) c. P(1 d. P(2 3 4 2.
> Suppose that the random variable x = weekly water usage (in gallons) for a randomly selected studio apartment in Los Angeles has the probability distribution described by the following density curve. a. What probability is represented by the shaded area
> An online store charges for shipping based on the weight of the items in an order. Define the random variable x = weight of a randomly selected order (in pounds) The density curve of x is shown here: Shade the area under the curve corresponding to each o
> Consider the population that consists of all soft contact lenses made by a particular manufacturer, and define the random variable x = thickness (mm). Suppose that a reasonable model for the probability distribution of x is the one shown in the following
> Let x denote the time (in seconds) necessary for an individual to react to a certain stimulus. Suppose the probability distribution of x is specified by the accompanying density curve. a. What is the height of the density curve above x = 0? (Hint: Tota
> Suppose that the random variable x = waiting time for service at a bank (in minutes) has the probability distribution described by the density curve pictured below. a. What probability is represented by the shaded area? b. Suppose the shaded area = 0.26
> Let x denote the lifetime (in thousands of hours) of a certain type of fan used in diesel engines. Suppose the density curve of x is as pictured. Shade the area under the curve corresponding to each of the following probabilities (draw a new curve for e
> A new battery’s voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found. Suppose that 80% of all batteries have accep
> A contractor is required by a county planning department to submit anywhere from one to five forms (depending on the nature of the project) when applying for a building permit. Let y be the number of forms required of the next applicant. Suppose the prob
> A business has six customer service telephone lines. Let x denote the number of lines in use at any given time. Suppose that the probability distribution of x is as follows: Write each of the following events in terms of x, and then calculate the probab
> Suppose that a computer manufacturer receives computer boards in lots of five. Two boards are selected from each lot for inspection. You can represent possible outcomes of the selection process by pairs. For example, the pair (1, 2) represents the select
> Of all airline flight requests received by a certain ticket broker, 70% are for domestic travel (D) and 30% are for international flights (I). Define x to be the number that are for domestic flights among the next three requests received. Assuming indepe
> A pizza shop sells pizzas in four different sizes. The 1000 most recent orders for a single pizza resulted in the following proportions for the various sizes: With x = the size of a pizza in a single-pizza order, the given table is an approximation to t
> Suppose x = the number of courses a randomly selected student at a certain university is taking. The probability distribution of x appears in the following table: a. What is P(x = 4)? b. What is P(x ≤ 4)? c. What is the probability
> Suppose that 20% of all homeowners in an earthquake prone area of California are insured against earthquake damage. Four homeowners are selected at random. Define the random variable x as the number among the four who have earthquake insurance. a. Find
> A restaurant has four bottles of a certain wine in stock. The wine steward does not know that two of these bottles (Bottles 1 and 2) are bad. Suppose that two bottles are ordered, and the wine steward selects two of the four bottles at random. Consider t
> Suppose that fund-raisers at a university call recent graduates to request donations for campus outreach programs. They report the following information for last year’s graduates: Three attempts were made to contact each graduate. A do
> Consider the random variable y = the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose the probability distribution of y is as follows: a. Only y values of 0, 1, 2, 3, and 4 have probabilities greater than 0. What is p (4)?
> Two six-sided dice, one red and one white, will be rolled. List the possible values for each of the following random variables. a. x = sum of the two numbers showing b. y = difference between the number on the red die and the number on the white die (r
> A person is asked to draw a line segment that they think is 3 inches long. The length of the line segment drawn will be measured and the value of x = (actual length + 3) will be calculated. a. What is the value of x for a person who draws a line segment
> State whether each of the following random variables is discrete or continuous. a. The number of courses a student is enrolled in b. The time spent completing a homework assignment c. The length of a person’s forearm d. The number of times out of 10
> A person stands at the corner marked A of the square pictured in the previous exercise and tosses a coin. If it lands heads up, the person moves one corner clockwise, to B. If the coin lands tails up, the person moves one corner counterclockwise, to D. T
> A point is randomly selected from the interior of the square pictured here: Let x denote the distance from the lower left-hand corner A to the selected point. What are possible values of x? Is x a discrete or a continuous variable? B C A D. 1 foot
> Classify each of the following random variables as either discrete or continuous: a. The fuel efficiency (miles per gallon) of an automobile b. The amount of rainfall at a particular location during the next year c. The distance that a person throws a
> A box contains four slips of paper marked 1, 2, 3, and 4. Two slips are selected without replacement. List the possible values for each of the following random variables: a. x = sum of the two numbers b. y = difference between the first and second numb
> Starting at a particular time, each car entering an intersection is observed to see whether it turns left (L), turns right (R), or goes straight ahead (S). The experiment terminates as soon as a car is observed to go straight. Let x denote the number of
> State whether each of the following random variables is discrete or continuous: a. The number of defective tires on a car b. The body temperature of a hospital patient c. The number of pages in a book d. The number of draws (with replacement) from a
> In a national sample of 1907 American adults, 1297 indicated that they own a smartphone (“technology Device ownership: 2015,” pew research center). Assume that it is reasonable to regard this sample as a random sample of adult Americans. Is it reasonable
> If a hurricane were headed your way, would you evacuate? The headline of a press release issued January 21, 2009, by the survey research company international communications research (icrsurvey.com) states, “Thirty-one Percent of People on High-Risk Coas
> The paper “effects of caffeine on repeated Sprint ability, reactive agility time, Sleep and next Day performance” (Journal of Sports Medicine and Physical Fitness [2010]: 455–464) describes an experiment in which male athlete volunteers who were consider
> Samples of both surface soil and subsoil were taken from eight randomly selected agricultural locations in a particular county. The soil samples were analyzed to determine surface pH and subsoil pH, with the results shown in the accompanying table. a.
> Here’s one to sink your teeth into: The authors of the article “analysis of food crushing Sounds During mastication: total Sound Level Studies” (Journal of Texture Studies [1990]: 165â€
> The paper “the truth about Lying in online Dating profiles” (Proceedings, Computer-Human Interactions [2007]: 1–4) describes an investigation in which 40 men and 40 women with online dating profiles a
> Head movement evaluations are important because disabled individuals may be able to operate communications aids using head motion. The paper “constancy of head turning recorded in healthy Young humans” (Journal of Biom
> The article “a Shovel with a perforated blade reduces energy expenditure required for Digging wet clay” (Human Factors, 2010: 492–502) described a study in which each of 13 workers performed a task us
> The paper referenced in the previous exercise also gave information on calorie content. For the sample of Burger King meal purchases, the mean number of calories was 1008, and the standard deviation was 483. For the sample of McDonald’s meal purchases, t
> The paper “Sodium content of Lunchtime fast food purchases at major U.S. chains” (Archives of Internal Medicine [2010]: 732–734) reported that for a random sample of 850 meal purchases made at Burger King, the mean sodium content was 1685 mg, and the sta
> Do male college students spend more time studying than female college students? This was one of the questions investigated by the authors of the paper “an ecological momentary assessment of the physical activity and Sedentary behaviour patterns of Univer
> For each of the following hypothesis testing scenarios, indicate whether or not the appropriate hypothesis test would be for a difference in population means. If not, explain why not. Scenario 1: The authors of the paper “adolescents and mp3 players: to
> Descriptions of three studies are given. In each of the studies, the two populations of interest are students majoring in science at a particular university and students majoring in liberal arts at this university. For each of these studies, indicate whe
> An individual can take either a scenic route to work or a nonscenic route. She decides that use of the nonscenic route can be justified only if it reduces the mean travel time by more than 10 minutes. a. If µ1 refers to the mean travel time for nonsceni
> Use the information in the previous exercise to construct a 95% bootstrap confidence interval to estimate the difference in mean one-year improvement in ADHD Severity Score for the ONTRAC treatment and the control treatment. Interpret the interval in con
> A new set of cognitive training modules called “ONTRAC” was developed to help children with attention deficit/hyperactivity disorder (ADHD) to improve focus and to more easily dismiss distractions (“t
> Use the information in the previous exercise to construct a 95% bootstrap confidence interval to estimate the mean difference in change in brain activity, HC − LC. Interpret the interval in context. You can use make use of the Shiny app
> Behavioral intervention treatments may affect perceptions of reward in human brains, and thus help people to manage weight loss. In one of the first studies relating brain activity related to rewards and weight loss, researchers recorded brain activity a
> Use the information in the previous exercise to construct a 95% bootstrap confidence interval to estimate the difference in mean Personal Meaning scores for patients with cancer in the high-dose and low-dose psilocybin groups. Interpret the interval in c
> Studies have been conducted to evaluate the effectiveness of psilocybin mushrooms on improving the quality of life for patients with cancer (“a Dose of a hallucinogen from a ‘magic mushroom,’ and then
> Use the information given in the previous exercise to construct a 95% bootstrap confidence interval to estimate the difference in mean average working heart rates for the driver in teams of two firefighters and the driver in teams of from three to five f
> The Sheboygan (Wisconsin) Fire Department received a report on the potential effects of reductions in the number of firefighters it employs (“Study of fire Department causes controversy,” USA ToDAy NETWoRK-Wisconsin, D
> Use the information given in the previous exercise to calculate a 95% bootstrap confidence interval to estimate the mean difference in movement, OFF – CL. Interpret the interval in context. You can use make use of the Shiny apps in the collection at stat
> New “closed loop” (CL) devices have been developed to help to suppress overactive brain activity in patients with conditions such as Parkinson’s disease and epilepsy (“conceptualizat
> The online article “Death metal in the operating room” (www.npr.org, December 24, 2009) describes an experiment investigating the effect of playing music during surgery. One conclusion drawn from this experiment was that doctors listening to music that c
